A generalized mathematical model for efficiency calibration of gamma detectors: Application to practical cases

Abstract

Ef fi ciency cal i bra tion, i. e. de ter mi na tion of de tec tion ef fi ciency, e p , is a cru cial is sue in gamma spec trom e try (quan ti fi ca tion of gamma spec tro scopic mea sure ments) with semi con duc tor and scin til la tion de tec tors. Com par ing three pos si ble ways to ad dress ing the prob lem-rel ative, ab so lute and semi em pir i cal-ad van tages of the lat ter are em pha sized. Among semi empir i cal mod els, ef fi ciency trans fer us ing ef fec tive solid an gles, W, is sorted out and briefly elabo rated. This ap proach re duces the prob lem of ef fi ciency cal i bra tion to the de ter mi na tion of W. It proved re li able and has been broadly used in prac tice, mainly in the form of the long exist ing AN GLE soft ware. Pro gress ing fur ther, a gen er al ized math e mat i cal for mula for cal cula tions is de vel oped-first of the kind-of fer ing an op por tu nity for ad vanced ap pli ca tions of gamma spec trom e try. The for mula en ables un lim ited flex i bil ity in ap pli ca tion, as it con veniently sep a rates the source data from the de tec tor data dur ing the in te gra tion pro ce dures (W cal cu la tions). Its prac ti cal ity is dem on strated for a num ber of typ i cally en coun tered count ing ar range ments, as well as for some ex otic ones. The rel e vant for mu lae are used in PC cal cu lations and nu mer i cal test ing is fur ther per formed so as to check the va lid ity of the math e mat ical method and the com puter code. Care was taken of the op ti mi za tion of com plex nu mer i cal pro ce dures em ployed (in volv ing five fold nu mer i cal in te gra tion), so as to keep com pu ta tion times as low as pos si ble (in or der of min utes or even sec onds on or di nary PC). Re sults obtained are af fir ma tive for both the method and the code. The model will be grad u ally in cor porated into AN GLE soft ware, thus mak ing it readily avail able for rou tine use by gamma spectrom e try com mu nity.